The manufacturing of integrated circuits aims for continuously decreasing feature sizes of the fabricated components. Semiconductor manufacturing includes repeatedly projecting a pattern in a lithographic step onto a semiconductor wafer and processing the wafer to transfer the pattern into a layer deposited on the wafer surface or into the substrate of the wafer. This processing includes depositing a resist film layer on the surface of the semiconductor substrate in a spin coating process, projecting a mask with the pattern onto the resist film layer and developing or etching the resist film layer to create a resist structure.
The resist structure is transferred into a layer deposited on the wafer surface or into the substrate in an etching step. Planarization and other intermediate processes may further be necessary to prepare a projection of a successive mask level. Furthermore, the resist structure can also be used as a mask during an implantation step. The resist mask defines regions in which the electrical characteristics of the substrate are altered by implanting ions.
The spin coating process can be subdivided in four different stages. First, resist material is deposited on the wafer. Many different ways of deposition exist, for a description see D. E. Bornside, C. W. Macosko, and L. E. Scriven, “On the Modeling of Spin Coating”, J. Imaging Technology, 13, pages 122-130, 1987. In a second stage, the spin-up step, the wafer rotates and the entire wafer surface is covered with resist liquid. In the third stage, the spin-off step, excess liquid is removed from the wafer. The liquid flows radially outward and flies off the edge of the rotating disk. During this stage steep wave fronts of the resist liquid can form but they run radially outward. Behind these fronts a film of nearly uniform thickness is established if the wafer surface is flat.
It is a characteristic feature of the spin coating process that when the resist film continues thinning the film surface has the tendency to become more and more uniform. The fourth stage consists of solidifying the resist material. Solvent has evaporated during the preceding stages and, therefore, the resist has meanwhile become so viscous that the loss rate of resist material due to the radial outflow has already reduced much. Thereafter, the mass loss due to ongoing solvent evaporation dominates the further thinning of the resist material.
Finally, if the spin coating time has exceeded a certain limit solvent evaporation also ceases. Further prolongation of the spinning time has no significant influence anymore. The film height approaches a steady state.
Thickness variations of photo resist films are highly undesirable during chip manufacturing. The reason being that the sizes of the structures that are lithographically to be imaged depend sensitively on the resist thickness. Varying resist thicknesses over the wafer can directly impact the chip yield. Usually, if the wafer substrate is flat, spin coating yields very uniform resist film surfaces. However, sometimes the wafer substrate is not flat but shows a distinctive topography. For instance, the necessity to coat a resist film directly on a given layer structure can arise due to economical reasons because it is time-consuming and expensive to planarize (to some extent) a wafer surface with an intermediate coating layer.
Experimentally, for spin coating over topographies, it can often be observed that although the wafer topographies are periodically repeated inside the chip areas on the wafer, the resist film's thickness variations after spin coating are not. The observed thickness varies not only as a function of the topography inside a single chip area, but also depends strongly on the wafer position of the chip. If the resist film height varies from chip to chip it becomes impossible to lithographically form the same structures inside the different chip areas on the wafer. The operating parameters during spin coating e.g. spin speed and initial viscosity have to be chosen such that this undesired wafer signature is minimized.
Besides the experimental observations as described above, many theoretical studies exist that try to model the spin coating process.
Historically, theoretical spin coating studies were initiated by the work of A. G. Emslie, F. T. Bonner, and L. G. Peck, “Flow of Viscous Liquid on a Rotating Disk”, J. Appl. Phys., Vol. 29, 5, pages 858-862, 1958 (hereinafter, “Emslie, et al.”). In this document, the flow behavior of the resist on a rotating disk is analyzed and the time-dependent film height is related to the resist flow beneath the surface. The velocity field inside the resist film has been derived in the framework of the lubrication approximation of the Navier-Stokes equations and the resist has been treated as an incompressible Newtonian liquid.
Emslie, et al. theoretically explained the experimental fact that a flat film surface results when a resist is spun on a flat rotating substrate and that initially non-uniform film profiles tend to become more and more uniform under centrifugation. Later on, the work of Emslie, et al. has been extended in many respects.
As one of the extensions, the document of S. Middleman, “The effect of induced air-flow on the spin coating of viscous liquids”, J. Appl. Phys., Vol. 62, 6, pages 2530-2532, 1987, (hereinafter, “Middleman”) should be mentioned. Importantly, Middleman incorporated the effect of shear stress at the resist-air interface on the rate of thinning of the film. The shearing stress at the resist-air interface results because the rotating disk, e.g., a semiconductor wafer, acts like a “centrifugal pump” or fan.
Due to the disk rotation and the friction between the air and the disk surface, the air above the disk gets a velocity component tangential to the disk circumference. This tangential velocity induces also a radial velocity component due to the centrifugal acceleration. The radial outflow of the air in turn results in a vertical air flow towards the disk. Of special interest is the fact that significant radially and tangentially directed shearing forces are generated by the air flow.
Middleman employed an existing analytical solution of the velocity field of the air given by W. G. Cochran, “The flow due to a rotating disk”, Proc. Cambridge Philos. Soc., 30, pages 365-375, 1934 (hereinafter, “Cochran”), and used this analytical expression for the radially directed shear stress to show that the shear stress has a significant influence on the rate of film thinning. The radially directed shear stress is given by
                              τ          rz          air                =                              1            2                    ⁢                      ω                          3              /              2                                ⁢                      μ            air                          1              /              2                                ⁢                      ρ            air                          1              /              2                                ⁢          r                                    (        1        )            where r is the radial coordinate on the disk, the component τrzair stands for the r-component of the force per unit area across a plane surface element normal to the z-direction, ω is the angular velocity of the rotating disk, and μair and ρair denote the dynamic viscosity and density of air, respectively.
The expression by Cochran for the tangentially acting stress reads
                                          τ                          Θ              ⁢                                                          ⁢              z                        air                    =                      -            0                          ,                  616          ⁢                      ω                          3              /              2                                ⁢                      μ            air                          1              /              2                                ⁢                      ρ            air                          1              /              2                                ⁢          r                                    (        2        )            where Θ is the azimuthal coordinate on the disk and the stress component τΘzair stands for the Θ-component of the force per unit area across a plane surface element normal to the z-direction.
The formulas (1) and (2) for the radial and tangential air shear above the wafer are accurate as long as a Reynolds-number criterion is met, in the formR2ωρair/μair<3×105  (3)
For a 300 mm wafer (radius r=15 cm), a spin speed ω=1300 rpm and the kinematic viscosity of air at normal conditions, the Reynolds number is 2.04×105, which is not too much under the above limit.
At higher spin speeds (ω>1900 rpm) turbulent air flow above the wafer sets in, which would degrade the spin coating performance. It should be noted, that the radial and tangential components τrzair and τΘzair can as well be expressed in the lateral Cartesian coordinate basis that is co-rotating with the wafer,
                                          τ            xz            air                    =                                    R              ·              x                        -                          T              ·              y                                      ⁢                                  ⁢        and        ⁢                                  ⁢                                            τ              yz              air                        =                                          R                ·                y                            +                              T                ·                x                                              ,                                          ⁢          where                ⁢                                  ⁢                  R          =                                    1              2                        ⁢                          ω                              3                /                2                                      ⁢                          μ              air                              1                /                2                                      ⁢                          ρ              air                              1                /                2                                                    ⁢                                  ⁢        and        ⁢                                  ⁢                  T          =                                    -              0                        ⁢                          ,                        ⁢            616            ⁢                          ω                              3                /                2                                      ⁢                          μ              air                              1                /                2                                      ⁢                          ρ              air                              1                /                2                                                                        (        4        )            
In the document of D. Meyerhofer, “Characteristics of resist films produced by spinning”, J. Appl. Phys., Vol. 49, 7, pages 3993-3997, 1978 (hereinafter, “Meyerhofer”), a spin coating model is presented including an evaporation rate of solvent during resist spinning. Meyerhofer proposed a solvent evaporation rate that is proportional to the square root of the angular velocity. Using this functional dependence of the evaporation rate on the spinning speed, Meyerhofer calculated model predicted time-dependent film heights for various spin speeds and compared to measured values.
In the documents of P. C. Sukanek, “Spin Coating”, J. Imaging Technology, Vol. 11, 4, pages 184-190, 1985 and P. C. Sukanek, “A model for Spin Coating with Topography”, J. Electrochem. Soc., Vol. 136, 10, pages 3019-3026, 1989 (collectively hereinafter, “Sukanek”), Meyerhofer's evaporation approach is further extended by accounting also for the dependence of the evaporation rate on solvent content and gas-phase resistance. Sukanek modeled the evaporation rate e with units mass/(time×area) ase=αω1/2(ρs−ρsres),  (5)where α is a constant and ρs denotes the mass density of the solvent. The parameter ρsres stands for the density of residual solvent that is known to remain in the film after spin coating. The residual solvent density in (5) is to be considered as an empirical quantity accounting approximately for the gas-phase resistance due to saturation above the film and the finally reduced solvent mobility inside the film.
Sukanek also included surface tension forces and surface tension gradients in his treatment. In Sukanek's treatment of spin coating over topographies both the pressure as well as the solvent content become functions of the lateral coordinates in the wafer plane. The surface tension coefficient and the viscosity depend on the local solvent content and are also spatially dependent. Sukanek's approach allowed taking into account the spatial variations of viscosity and surface tension coefficient.
Other approaches for spin coating over topographical wafer surfaces have been disclosed by P. -Y. Wu and F. -C. Chou, “Complete analytical solutions of film planarization during spincoating”, J. Electrochem. Soc., Vol. 146, 10, pages 3819-3826, 1999, F. -C. Chou and P. -Y. Wu, “Effect of air shear on film planarization during spin coating”, J. Electrochem. Soc., Vol. 147, 2, pages 699-705, 2000, S. Kim, J. S. Kim, and F. Ma, “On the flow of a thin liquid film over a rotating disk”, J. Appl. Phys., Vol. 69, 4, pages 2593-2601, 1981, and J. S. Kim, S. Kim, and F. Ma, “Topographic effect of surface roughness on thin-film flow”, J. Appl. Phys., Vol. 73, 1, pages 422-428, 1993.
A conceptional advantage compared to other approaches is Sukanek's treatment of solvent evaporation and of local surface tension and viscosity gradients, which are a consequence of topographically induced perturbations of the solvent flow during spin coating. During the time evolution these effects are coupled to the film height evolution.
The above-described methods are, however, to some extent approximations that rely on certain assumptions. Further investigations might be necessary to provide more detailed results for studying resist film variations of a topography on a wafer.